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On this page are computer-accessible forms for the graph C4[ 128, 56 ] = SS[128,19].

(I) Following is a form readable by MAGMA:

g:=Graph<128|{ {1, 3}, {116, 118}, {28, 30}, {1, 2}, {29, 30}, {1, 5}, {115, 119}, {113, 117}, {26, 30}, {1, 4}, {27, 30}, {22, 31}, {114, 120}, {18, 31}, {17, 31}, {112, 126}, {76, 92}, {111, 127}, {109, 125}, {106, 122}, {105, 121}, {68, 85}, {102, 119}, {100, 117}, {73, 88}, {69, 84}, {71, 84}, {101, 118}, {69, 81}, {99, 119}, {75, 95}, {70, 82}, {71, 83}, {66, 87}, {76, 89}, {75, 94}, {70, 83}, {75, 93}, {77, 91}, {64, 87}, {108, 123}, {107, 124}, {97, 118}, {77, 90}, {65, 86}, {72, 81}, {72, 82}, {98, 120}, {67, 88}, {74, 86}, {104, 117}, {73, 87}, {74, 85}, {103, 120}, {96, 127}, {15, 47}, {94, 126}, {93, 125}, {91, 123}, {89, 121}, {79, 111}, {17, 49}, {16, 48}, {26, 59}, {79, 110}, {29, 60}, {27, 58}, {11, 41}, {6, 37}, {78, 109}, {24, 59}, {28, 56}, {76, 104}, {25, 60}, {88, 125}, {28, 57}, {10, 44}, {92, 122}, {90, 124}, {13, 43}, {12, 42}, {24, 63}, {25, 62}, {14, 38}, {82, 122}, {81, 121}, {77, 101}, {29, 53}, {21, 61}, {15, 39}, {65, 105}, {66, 106}, {67, 107}, {68, 108}, {6, 47}, {87, 126}, {86, 127}, {78, 100}, {22, 61}, {77, 102}, {76, 103}, {75, 96}, {18, 62}, {79, 99}, {27, 55}, {26, 54}, {22, 58}, {19, 63}, {15, 34}, {79, 98}, {14, 32}, {23, 57}, {64, 110}, {7, 40}, {84, 123}, {83, 124}, {78, 97}, {9, 38}, {8, 39}, {7, 55}, {28, 44}, {8, 56}, {16, 33}, {27, 42}, {6, 53}, {26, 41}, {19, 32}, {17, 37}, {23, 35}, {21, 33}, {7, 50}, {22, 35}, {20, 34}, {29, 43}, {23, 32}, {11, 51}, {25, 33}, {21, 45}, {16, 40}, {12, 52}, {8, 49}, {80, 105}, {20, 45}, {9, 48}, {24, 34}, {80, 106}, {80, 107}, {14, 50}, {80, 108}, {24, 36}, {18, 46}, {19, 46}, {25, 36}, {10, 52}, {78, 112}, {13, 51}, {9, 54}, {9, 73}, {50, 114}, {48, 113}, {8, 74}, {42, 104}, {49, 115}, {51, 113}, {11, 72}, {12, 72}, {45, 104}, {38, 96}, {52, 114}, {51, 116}, {52, 115}, {10, 66}, {45, 101}, {46, 102}, {15, 70}, {44, 101}, {46, 103}, {13, 71}, {42, 96}, {58, 112}, {14, 69}, {13, 65}, {47, 99}, {7, 74}, {10, 71}, {43, 102}, {41, 103}, {6, 73}, {12, 67}, {11, 68}, {63, 112}, {18, 66}, {34, 114}, {19, 67}, {49, 97}, {21, 68}, {53, 100}, {33, 115}, {48, 98}, {60, 110}, {61, 111}, {56, 107}, {62, 109}, {17, 69}, {32, 116}, {20, 64}, {55, 99}, {57, 109}, {59, 111}, {20, 65}, {16, 70}, {50, 100}, {23, 64}, {54, 97}, {53, 108}, {56, 98}, {47, 116}, {55, 106}, {54, 105}, {61, 88}, {62, 86}, {58, 83}, {63, 85}, {57, 82}, {60, 81}, {31, 113}, {59, 84}, {5, 117}, {40, 91}, {44, 95}, {2, 119}, {3, 118}, {40, 94}, {43, 93}, {41, 94}, {35, 91}, {36, 92}, {3, 122}, {5, 124}, {4, 125}, {37, 92}, {35, 89}, {37, 95}, {39, 93}, {2, 121}, {2, 126}, {4, 120}, {3, 127}, {38, 90}, {36, 90}, {39, 89}, {4, 123}, {5, 128}, {85, 128}, {95, 128}, {110, 128} }>;

(II) A more general form is to represent the graph as the orbit of {1, 3} under the group generated by the following permutations:

a: (1, 30)(2, 27)(3, 26)(4, 28)(5, 29)(6, 85)(7, 87)(8, 88)(9, 86)(10, 91)(11, 92)(12, 89)(13, 90)(14, 20)(15, 19)(16, 18)(17, 21)(22, 115)(23, 114)(24, 116)(25, 113)(31, 33)(32, 34)(35, 52)(36, 51)(37, 68)(38, 65)(39, 67)(40, 66)(41, 122)(42, 121)(43, 124)(44, 123)(45, 69)(46, 70)(47, 63)(48, 62)(49, 61)(50, 64)(53, 128)(54, 127)(55, 126)(56, 125)(57, 120)(58, 119)(59, 118)(60, 117)(71, 77)(72, 76)(73, 74)(75, 80)(78, 79)(81, 104)(82, 103)(83, 102)(84, 101)(93, 107)(94, 106)(95, 108)(96, 105)(97, 111)(98, 109)(99, 112)(100, 110)
b: (1, 31, 80, 33)(2, 113, 106, 21)(3, 22, 105, 16)(4, 17, 107, 25)(5, 18, 108, 115)(6, 12, 110, 103)(7, 101, 112, 13)(8, 90, 109, 84)(9, 82, 111, 89)(10, 85, 102, 100)(11, 99, 104, 87)(14, 28, 24, 93)(15, 96, 23, 26)(19, 29, 114, 95)(20, 94, 116, 27)(30, 34, 75, 32)(35, 54, 70, 127)(36, 125, 69, 56)(37, 67, 60, 120)(38, 57, 59, 39)(40, 118, 58, 65)(41, 47, 42, 64)(43, 50, 44, 63)(45, 126, 51, 55)(46, 53, 52, 128)(48, 122, 61, 121)(49, 124, 62, 123)(66, 68, 119, 117)(71, 74, 77, 78)(72, 79, 76, 73)(81, 98, 92, 88)(83, 86, 91, 97)
c: (2, 3)(4, 5)(6, 8)(7, 9)(10, 13)(11, 12)(14, 16)(15, 17)(18, 20)(19, 21)(22, 24)(23, 25)(26, 27)(28, 29)(31, 34)(32, 33)(35, 36)(37, 39)(38, 40)(41, 42)(43, 44)(45, 46)(47, 49)(48, 50)(51, 52)(53, 56)(54, 55)(57, 60)(58, 59)(61, 63)(62, 64)(65, 66)(67, 68)(69, 70)(73, 74)(78, 79)(81, 82)(83, 84)(85, 88)(86, 87)(89, 92)(90, 91)(93, 95)(94, 96)(97, 99)(98, 100)(101, 102)(103, 104)(105, 106)(107, 108)(109, 110)(111, 112)(113, 114)(115, 116)(117, 120)(118, 119)(121, 122)(123, 124)(125, 128)(126, 127)
d: (1, 35, 78, 69, 30, 52, 79, 45)(2, 22, 97, 84, 28, 114, 110, 104)(3, 91, 109, 14, 29, 12, 99, 21)(4, 23, 100, 81, 27, 115, 111, 101)(5, 89, 112, 17, 26, 10, 98, 20)(6, 11, 106, 16, 86, 90, 93, 19)(7, 25, 96, 102, 88, 116, 108, 82)(8, 24, 95, 103, 87, 113, 105, 83)(9, 13, 107, 15, 85, 92, 94, 18)(31, 54, 71, 56, 34, 128, 76, 126)(32, 53, 72, 55, 33, 127, 77, 125)(36, 75, 46, 73, 51, 80, 70, 74)(37, 41, 66, 48, 65, 124, 39, 63)(38, 43, 67, 47, 68, 122, 40, 62)(42, 119, 61, 118, 123, 57, 50, 60)(44, 120, 64, 117, 121, 58, 49, 59)
e: (1, 37)(2, 6)(3, 95)(4, 17)(5, 92)(7, 23)(8, 109)(9, 102)(10, 111)(12, 21)(13, 26)(14, 91)(15, 112)(16, 19)(18, 98)(20, 27)(22, 114)(24, 83)(25, 107)(28, 86)(29, 105)(30, 65)(31, 120)(32, 40)(33, 67)(34, 58)(35, 50)(36, 124)(38, 77)(39, 78)(41, 51)(42, 45)(43, 54)(44, 127)(46, 48)(47, 126)(49, 125)(52, 61)(53, 121)(55, 64)(56, 62)(57, 74)(59, 71)(60, 80)(63, 70)(66, 79)(68, 72)(69, 123)(73, 119)(75, 118)(76, 117)(81, 108)(82, 85)(87, 99)(88, 115)(89, 100)(93, 97)(94, 116)(96, 101)(103, 113)(106, 110)(122, 128)
f: (2, 5)(3, 4)(6, 7)(8, 9)(10, 11)(12, 13)(14, 15)(16, 17)(18, 21)(19, 20)(22, 25)(23, 24)(26, 28)(27, 29)(31, 33)(32, 34)(35, 36)(37, 40)(38, 39)(41, 44)(42, 43)(45, 46)(47, 50)(48, 49)(51, 52)(53, 55)(54, 56)(57, 59)(58, 60)(61, 62)(63, 64)(65, 67)(66, 68)(69, 70)(71, 72)(73, 74)(76, 77)(78, 79)(81, 83)(82, 84)(85, 87)(86, 88)(89, 90)(91, 92)(93, 96)(94, 95)(97, 98)(99, 100)(101, 103)(102, 104)(105, 107)(106, 108)(109, 111)(110, 112)(113, 115)(114, 116)(117, 119)(118, 120)(121, 124)(122, 123)(125, 127)(126, 128)

(III) Last is Groups&Graphs. Copy everything between (not including) the lines of asterisks into a plain text file and save it as "graph.txt". Then launch G&G (Groups&Graphs) and select Read Text from the File menu.

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&Graph
C4[ 128, 56 ]
128
-1 2 3 4 5
-2 121 1 126 119
-3 1 122 127 118
-4 1 123 125 120
-5 1 124 117 128
-6 47 37 73 53
-7 55 50 40 74
-8 56 49 39 74
-9 48 38 73 54
-10 44 66 71 52
-11 68 72 51 41
-12 67 72 52 42
-13 71 51 43 65
-14 69 38 50 32
-15 34 47 70 39
-16 33 48 70 40
-17 69 37 49 31
-18 66 46 62 31
-19 67 46 63 32
-20 34 45 64 65
-21 33 45 68 61
-22 35 58 61 31
-23 35 57 64 32
-24 34 36 59 63
-25 33 36 60 62
-26 59 30 41 54
-27 55 58 30 42
-28 44 56 57 30
-29 60 30 53 43
-30 26 27 28 29
-31 22 113 17 18
-32 23 14 116 19
-33 25 16 115 21
-34 24 15 114 20
-35 22 23 89 91
-36 24 90 25 92
-37 92 6 17 95
-38 90 14 96 9
-39 89 15 93 8
-40 91 16 94 7
-41 11 26 103 94
-42 12 27 104 96
-43 13 102 93 29
-44 101 28 95 10
-45 101 104 20 21
-46 102 103 18 19
-47 99 15 6 116
-48 113 16 9 98
-49 115 17 8 97
-50 100 14 114 7
-51 11 13 113 116
-52 12 114 115 10
-53 100 6 29 108
-54 26 105 9 97
-55 99 27 7 106
-56 28 8 107 98
-57 23 82 28 109
-58 22 112 27 83
-59 111 24 26 84
-60 110 25 81 29
-61 22 88 111 21
-62 25 18 86 109
-63 24 112 19 85
-64 110 23 20 87
-65 13 105 20 86
-66 18 106 10 87
-67 88 12 19 107
-68 11 85 108 21
-69 14 81 17 84
-70 15 16 82 83
-71 13 83 84 10
-72 11 12 81 82
-73 88 6 9 87
-74 7 8 85 86
-75 93 94 95 96
-76 89 92 103 104
-77 90 101 91 102
-78 100 112 97 109
-79 99 110 111 98
-80 105 106 107 108
-81 121 69 60 72
-82 122 57 70 72
-83 58 124 70 71
-84 123 69 59 71
-85 68 128 63 74
-86 127 62 74 65
-87 66 126 73 64
-88 67 125 61 73
-89 121 35 39 76
-90 77 36 124 38
-91 77 35 123 40
-92 122 36 37 76
-93 125 39 75 43
-94 126 40 41 75
-95 44 37 128 75
-96 38 127 42 75
-97 78 49 118 54
-98 56 79 48 120
-99 55 79 47 119
-100 78 50 117 53
-101 44 77 45 118
-102 77 46 119 43
-103 46 41 76 120
-104 45 117 42 76
-105 121 80 54 65
-106 55 66 122 80
-107 56 67 80 124
-108 68 123 80 53
-109 78 57 125 62
-110 79 60 128 64
-111 79 59 61 127
-112 78 58 126 63
-113 48 51 117 31
-114 34 50 52 120
-115 33 49 52 119
-116 47 51 118 32
-117 100 113 5 104
-118 101 3 116 97
-119 99 2 102 115
-120 4 103 114 98
-121 89 2 81 105
-122 3 92 82 106
-123 91 4 84 108
-124 90 5 83 107
-125 88 4 93 109
-126 2 112 94 87
-127 111 3 96 86
-128 110 5 95 85
0

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